Tensor deconvolution: A method to locate equivalent sources from full tensor gravity data

Abstract

We present a method dedicated to the interpretation of full tensor ͑gravity͒ gradiometry ͑FTG͒ data called tensor deconvolution. It is especially designed to benefit from the simultaneous use of all the FTG components and of the gravity field. In particular, it uses tensor scalar invariants as a basis for source location. The invariant expressions involve all of the independent components of the tensor. This method is a tensor analog of Euler deconvolution, but has the following advantages compared to the conventional Euler deconvolution method: ͑1͒ It provides a solution at every observation point, without the use of a sliding window. ͑2͒ It determines the structural index automatically; as a consequence, the structural index follows the variations of the field morphology. ͑3͒ It uses all components of the measured full gradient tensor and gravity field, thus reducing errors caused by random noise. It is based on scalar invariants that are by nature insensitive to the orientation of the measuring device. We tested our method on both noise-free and noise-contaminated data. These tests show that tensor solutions cluster in the vicinity of the center of causative bodies, whereas Euler solutions better outline their edges. Hence, these methods should be combined for improved contouring and depth estimation. In addition, we use a clustering method to improve the selection of solutions, which proves advantageous when data are noisy or when signals from close causative bodies interfere.

New techniques for estimation of source parameters: Applications to airborne gravity and pseudo-gravity gradient tensors

“…Their method uses the full GGT and the components of the gravity vector to provide additional constraints on the Euler solutions. Mikhailov et al (2007) combined scalar invariants of the tensor and Euler deconvolution to locate equivalent sources. They showed that their method, the so-called tensor deconvolution, is rather insensitive to random noise in the different tensor components and a solution is found at all individual observation points without use of sliding windows.…”

“…In recent years, several new techniques for interpretation of GGT data have been introduced in the literature (e.g. Pedersen and Rasmussen, 1990;Vasco and Taylor, 1991;Edwards et al, 1997;Routh et al, 2001;Zhdanov et al, 2004;Droujinine et al, 2007;While et al, 2006;Mikhailov et al, 2007;Pajot et al, 2008;While et al, 2009;Beiki and Pedersen, 2010;Beiki, 2010). However, both processing and interpretation of GGT data are still challenging and requires further development.…”

Determining the depth of certain gravity sources without a priori specification of their structural index

“…Mathematical properties of gravity gradient tensors suggest new processing and interpretation techniques. In recent years, several new techniques for interpretation of gravity tensor data have been introduced in the literature (Pedersen and Rasmussen, 1990;Zhang et al, 2000;Mikhailov et al, 2007;Beiki and Pedersen, 2010;Beiki, 2010;Cooper, 2014), and these methods belong to semiautomatic interpretation techniques, which have a fast computation speed. Some other publications have applied an inversion process to the tensor data for model construction representing the subsurface anomalies (Li, 2001;Zhdanov et al, 2004).…”

Window constrained inversion of gravity gradient tensor data using dike and contact models

“…GGT data can be measured either using land, airborne, marine, or space platforms. In recent years, new techniques for processing and interpretation of GGT data have been developed (e.g., Pedersen and Rasmussen, 1990;Vasco and Taylor, 1991;Zhdanov et al, 2004;Mikhailov et al, 2007;FitzGerald et al, 2009;Beiki, 2010;Beiki and Pedersen, 2010). In 1990, Pedersen and Rasmussen studied Formerly Uppsala University, Department of Earth Sciences, Uppsala, Sweden; currently CSIRO Earth Science and Resource Engineering, North Ryde, NSW, Australia.…”